Lang's aforementioned conjecture predicts that, for any abelian variety \(A\)  over a number field \(K\)  with \(A(K)\)  dense and any ramified cover \(\pi :X\rightarrow A\) , the set \(A(K)\setminus \pi (X(K))\)  is again dense. Motivated by the inverse Galois problem, Serre also raised a related question [1]}, a positive answer to which would lead to the same conclusion.
Our main results stated below (see Theorem REF  and Theorem REF ) confirm the density of \(A(K)\setminus \pi (X(K))\)  unconditionally for all abelian varieties, and thereby provide novel evidence for Lang's conjectures on rational points and answer in part Serre's question.
